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In this paper, we prove two fixed point theorems in the setting of orthogonal complete metric spaces via τ-distances. Our theorems generalize and improve many known results in the literature (see, for example Refs. [6, theorem 4.2] and [3, theorem 3]).

In this development, we present some fixed point theorems for condensing multivalued mappings in the setting of Banach spaces via measure of noncompactness, without adding regularity. Our results upgrade and extend many theorems in the literature. Moreover, an application to differential inclusions is given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this work, we define a new notion of μ F -contraction in Banach spaces, by modeling with measure of non-compactness the well-known concept of F -contraction given by Wardowski in metric spaces. We prove a fixed-point theorem and a common fixed-point theorem for our contraction. Our results extend the well-known Darbo contraction principle and large contractions in the literature. Furthermore, the paper contains examples and applications that show the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we first prove a new common fixed point in general topological spaces with a τ -distance. From this result, we establish two common fixed points for two new classes of contractive selfmappings in complete bounded metric spaces. Furthermore, an application to a system of differential equations and another to a system of functional equations arising in dynamic programming are given. [ABSTRACT FROM AUTHOR]

In the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results. [ABSTRACT FROM AUTHOR]

In the present paper, we analyze and study the control of a static thermoelastic contact problem. We consider a model which describes a frictional contact problem between a thermoelastic body and a deformable heat conductor obstacle. We derive a variational formulation of the model which is in the form of a coupled system of the quasi-variational inequality of elliptic type for the displacement and the nonlinear variational equation for the temperature. Then, under a smallness assumption, we prove the existence of a unique weak solution to the problem. Moreover, we establish the dependence of the solution with respect to the data and prove a convergence result. Finally, we introduce an optimization problem related to the contact model for which we prove the existence of a minimizer and provide a convergence result. [ABSTRACT FROM AUTHOR]